Combine ground beef, ginger, cumin, salt, cinnamon, cayenne and black pepper. Divide into six equal portions. Hand shape portions into square patties that are the same width as the rolls. Brush grill rack with oil. Grill patties for 4-6 minutes per side, flipping patties only once. During final two minutes of grilling, place rolls, cut side down, on the grill rack until lighty toasted.

On each roll bottom, place three layers of lettuce, a patty and an equal portion of the topping. Add roll tops. Cut finished burgers diagonally and serve.